What we believe about a bow is, generally speaking, what the bow will do in our hands. When someone says that they just can't shoot a particular style of bow accurately, it is almost certain that they had that belief before they picked up the bow, based on the statements of others, or of some brief encounter with a bow that created an unsatisfying memory.
Mass weight of a bow can contribute to the feeling of greater stability, but in the long run it is all about what we have become adapted to. Having said that, if you can shoot a bow with a very light mass weight and shoot it well, say a 52" sinew backed juniper selfbow which weights practically nothing, your bodies neurological and muscular adaptation to that bow will serve you well when shooting a heavier mass weight bow. The opposite would not be true.
No matter what type of bow you shoot, a rock steady bow arm is critical.The arrow shelf must remain still during the shot, and release must be smooth and consistent. Let me say that again; the arrow shelf must remain still and release must be smooth and consistent. It sounds so obvious, but these two basic skills often become overlooked in the hunt for the perfect bow.
If you can achieve these two basic skills, the type of bow in your hand will become less and less of an issue. Our ability to be accurate with a given bow is always more about us as archers and less about our equipment.
Go to Dean Torges website and read "The Elements Of Style" for the most concise treatise on shooting a bow; any bow.
http://www.bowyersedge.com/elements.html